A note on generalized po-bi-quasi Γ-ideals in po-bi-ternary Γ-semigroups

The aim of this paper is to study po-bi-ternary Γ-semigroups that satisfies the compatibility condition. Here, we introduced po-bi quasi-Γ-ideals, po-bi-Γ-ideals and generalized po-bi quasi-Γ-ideals in po-bi-ternary Γ-semigroups. Also, we define po-bi α-right Γ-ideals, po-bi (ξ, ζ)-lateral Γ-ideals and po-bi β-left Γ-ideals in po-bi-ternary Γ-semigroups. Some intersection properties of po-bi (α, (ξ, ζ), β)-quasi Γ-ideals have been investigated. Moreover, we introduced these notions in terms of minimal po-bi (α, (ξ, ζ), β)-quasi-Γ-ideals in po-bi-ternary Γ-semigroups. Finally, α-right simple, (ξ, ζ)-lateral simple, β-left simple, and (α, (ξ, ζ), β)-quasi simple po-bi-ternary Γ-semigroups are introduced and some of its properties have been discussed.